What is the largest average velocity of blood flow in an artery of radius $$4×10^{-3}$$​ m if the flow must remain laminar? Also determine the corresponding flow rate?

(Consider viscosity of blood to be $$2.084×10^{-3}$$​ pa s.)

Correct option is B

​$$\textbf{Given:} \\\mu = 2.084 \times 10^{-3} \, \text{Pa} \cdot \text{s} \\\rho = 1.06 \times 10^3 \, \text{kg/m}^3 \\\text{Radius of artery} = 4 \times 10^{-3} \, \text{m} \Rightarrow \text{Diameter} = d = 8 \times 10^{-3} \, \text{m} \\\text{Reynolds number for laminar flow: } R_e = 2000 \\[10pt]\text{Reynolds number formula:} \\R_e = \frac{\rho v D}{\mu} \\[10pt]\Rightarrow 2000 = \frac{1.06 \times 1000 \times v \times 8 \times 10^{-3}}{2.084 \times 10^{-3}} \\[10pt]\Rightarrow v = 0.49 \, \text{m/s} \\[10pt]\text{So, the largest average velocity of blood flow is } \boldsymbol{0.49 \, \text{m/s}} \\[10pt]\text{Flow rate } Q = A \cdot v \\[5pt]A = \pi r^2 = \pi (4 \times 10^{-3})^2 = 5.026 \times 10^{-5} \, \text{m}^2 \\[10pt]Q = 0.49 \times 5.026 \times 10^{-5} = 2.46 \times 10^{-5} \, \text{m}^3/\text{s} \\[10pt]\boxed{Q = 2.46 \times 10^{-5} \, \text{m}^3/\text{s}}$$​​